Description

We consider wave propagation in slender elastic waveguides. With aim at finding all vibration modes of such bodies, we develop a theoretical framework for application of energy principles and subsequent discretization of the problem using the finite-element method. We obtain a discrete set of solutions for propagating and evanescent branches and we examine the solution behavior in some detail. Finally, we compare the results with the analytic solutions of Pochhammer-Chree equations and conduct an accuracy and convergence study, determining the combination of mesh parameters and frequency regimes for which our code yields accurate results.